The role of problem representation and feature knowledge in algebraic equation-solving

Booth, Julie L.; Davenport, Jodi L.

doi:10.1016/j.jmathb.2013.04.003

Cited by 36 publications

(48 citation statements)

References 24 publications

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“…Middle‐school students’ errors in using the equal sign (e.g., moving or deleting the equal sign) are associated with poorer performance on end‐of‐year achievement tests, and have been deemed a ‘troublesome sign for students’ math achievement’ (Booth, Barbieri, Eyer, & Paré‐Blagoev, ; p. 19). Thus, instructional support for encoding equations – specifically, for encoding the equal sign – may contribute positively to students’ later math achievement (but see Booth & Davenport, , for an alternative view).…”

Section: Discussionmentioning

confidence: 99%

Perceptual support promotes strategy generation: Evidence from equation solving

Alibali

Crooks

McNeil

2017

British J of Dev Psycho

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Over time, children shift from using less optimal strategies for solving mathematics problems to using better ones. But why do children generate new strategies? We argue that they do so when they begin to encode problems more accurately; therefore, we hypothesized that perceptual support for correct encoding would foster strategy generation. Fourth-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) in a pre-test. They were then randomly assigned to one of three perceptual support conditions or to a Control condition. Participants in all conditions completed three mathematical equivalence problems with feedback about correctness. Participants in the experimental conditions received perceptual support (i.e., highlighting in red ink) for accurately encoding the equal sign, the right side of the equation, or the numbers that could be added to obtain the correct solution. Following this intervention, participants completed a problem-solving post-test. Among participants who solved the problems incorrectly at pre-test, those who received perceptual support for correctly encoding the equal sign were more likely to generate new, correct strategies for solving the problems than were those who received feedback only. Thus, perceptual support for accurate encoding of a key problem feature promoted generation of new, correct strategies. Statement of Contribution What is already known on this subject? With age and experience, children shift to using more effective strategies for solving math problems. Problem encoding also improves with age and experience. What the present study adds? Support for encoding the equal sign led children to generate correct strategies for solving equations. Improvements in problem encoding are one source of new strategies.

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Section: Discussionmentioning

confidence: 99%

Perceptual support promotes strategy generation: Evidence from equation solving

Alibali

Crooks

McNeil

2017

British J of Dev Psycho

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“…Misconceptions about the negative sign have been found to prevent students from succeeding in high level algebra and later mathematics (Prather & Alibali, 2008). Additionally, incorrect knowledge of equation features, such as the negative sign, has been found to be inversely correlated with students' procedural correctness (Booth & Davenport, 2013), predictive of the types of errors they make (Booth & Koedinger, 2008), and associated with their overall problem solving abilities (Knuth, Stephens, McNeil, & Alibali, 2006). Thus, ensuring students have proper knowledge about negative numbers, both their polarity sign and magnitude, should remain a topic in future research.…”

Section: Discussionmentioning

confidence: 99%

“…The Common Core mathematics standards call for students to begin to learn about a rational number system in the 6 th grade (approximately 11 years of age); previously their number knowledge focused on positive numbers within the base-10 system. This new inclusive number system is one where students will need to "apply and extend [their] Eighth grade is a critical time point for knowledge of negative numbers as this is when many students are beginning to learn algebra, a type of math that is thought to require the understanding of the negative sign for success in general and, more specifically, to solve equations properly (Booth & Davenport, 2013). Thus, ideally, students should be proficient with negatives by the 8 th grade, meaning they have developmentally increased their negative number magnitude knowledge within the 6 th and 7 th grade school years.…”

Section: Students' Understanding Of Negative Number Magnitudesmentioning

confidence: 99%

Student Magnitude Knowledge of Negative Numbers

Young

Booth

2015

J. Numer. Cogn.

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Numerous studies have demonstrated the relevance of magnitude estimation skills for mathematical proficiency, but little research has explored magnitude estimation with negative numbers. In two experiments the current study examined middle school students' magnitude knowledge of negative numbers with number line tasks. In Experiment 1, both 6th (n = 132) and 7th grade students (n = 218) produced linear representations on a -10,000 to 0 scale, but the 7th grade students' estimates were more accurate and linear. In Experiment 2, the 7th grade students also completed a -1,000 to 1,000 number line task; these results also indicated that students are linear for both negative and positive estimates. When comparing the estimates of negative and positive numbers, analyses illustrated that estimates of negative numbers are less accurate than those of positive numbers, but using a midpoint strategy improved negative estimates. These findings suggest that negative number magnitude knowledge follows a similar pattern to positive numbers, but the estimation performance of negatives lags behind that of positives.

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“…We focused on children's equal sign interpretation because it is widely regarded as important for success in algebra (e.g., Alibali, Knuth, Hattikudur, McNeil, & Stephens, 2007;Booth & Davenport, 2013;Carpenter, Franke, & Levi, 2003;McNeil & Alibali, 2005a, b). The equal sign (=) is a relational symbol, indicating that the two sides of an equation are equal and interchangeable (Kieran, 1981); however, children tend to view the equal sign operationally, meaning "add up the numbers" or "the answer" (Baroody & Ginsburg, 1983;Behr, Erlwanger, & Nichols, 1980;De Corte & Verschaffel, 1981;Kieran, 1981;Matthews & Rittle-Johnson, 2009;McNeil & Alibali, 2005a;Oksuz, 2007;Perry, 1991;Sáenz-Ludlow & Walgamuth, 1998).…”

Section: Introductionmentioning

confidence: 99%